Mitt Romney refused to apologise on Tuesday for describing 47% of Americans as government-dependent "victims" in a covertly recorded video that has thrown his presidential campaign into disarray.

In an attempt to save his campaign from ruin, Romney went on the Republican-friendly Fox News network just as the rightwing Drudge Report published excerpts from a 1998 tape showing Barack Obama favouring "redistribution".

The apparently co-ordinated attempt to stem the crisis from the video, published on the Mother Jones website, followed a stumbling press conference on Monday night in which Romney tried to defend comments made at a fundraiser in Florida.

Asked on Fox News if he had "kissed half the electorate goodbye" with the comments, Romney said: "I'm talking about the perspective of voters who I'm not likely to get to support me. Those who are dependent on government, and those who think government's job is to redistribute … I'm not going to get them."

He acknowledged that some people do not pay income tax – the figure is actually 46% – for good reason: "There are a number of retirees, members of the military who aren't paying taxes and that's as it should be.

"I think people would like to be paying taxes. The problem is that so many people have fallen into poverty that they're not paying taxes, [and] they're relying on government."

The revelations, which have forced the Romney campaign on to the defensive for the second week in succession, were met with dismay from conservative commentators and strategists, with one influential editor describing Romney's views as "stupid".

His campaign team, with their candidate already trailing Barack Obama after a long list of self-inflicted gaffes over the summer, is anxiously awaiting the next batch of polls to see the extent of the fallout.

The video was shot during an hour-long appearance by Romney in May at a $50,000-a-head fund-raising dinner at the Florida home of investment banker Marc Leder. More excerpts are being lined up for release, making it impossible for his campaign to dampen the firestorm and return to its core focus, the economy.

The latest clip shows Romney dismissing the chances of peace in the Israeli-Palestinian conflict, not an unusual view, but he then goes on to firmly put the blame solely on the Palestinians.

He contentiously described the the Palestinians as "committed to the destruction and elimination" of Israel and indicated he was unlikely to pursue, as president, the creation of a Palestinian state, warning that Iran would use it as a base for attacks on Israel.

The Israeli-Palestinian excerpt can be easily brushed aside by the Romney campaign but the 47% excerpt which was released on Monday is harder to handle.

Within the space of a few minutes, Romney managed to potentially offend the elderly, veterans, students, Latinos and other demographic groups, most of whom do, in fact, pay some taxes and have earned their entitlements.

In a remark that sounded especially callous from someone who claims that as president he would represent all Americans, he said: "My job is not to worry about those people."

One of the most destructive aspects of the video is the contrast between what he says in public and in private, opening him up to accusations of hypocrisy.

The release of the video came only hours after the Romney team, struggling in the polls and repeatedly forced on the defensive by the Obama campaign team, had announced it was rebooting its campaign.

The new-look strategy, in which Romney was to set out specific policies rather than focusing on attacking Obama, barely lasted 12 hours before the video emerged and the Romney campaign team was again engaged in damage-control.

The media coverage was almost entirely negative. The New York Daily News on its front page had the headline "Mitt Hits The Fan".

The Obama campaign was quick to jump on Romney's 47% remarks, with White House press secretary Jay Carney telling reporters on Tuesday that Obama was the president of all the people, not just those who voted for him. That was followed up with a new Obama campaign video in which footage from the 47% video was intercut with members of the public responding to it. "I actually felt sick to my stomach," said one woman.

But it is the reaction of conservatives that will cause the Romney campaign the most concern. Some are labelling his election run as the most inept they have seen in half a century.

The influential editor of the conservative Weekly Standard William Kristol described Romney's comments about the 47% as "arrogant and stupid" and hinted he should stand down in favour of his a ticket headed by his running mate Paul Ryan, with senator Marco Rubio as his vice-presidential candidate.

Mark McKinnon, who was one of John McCain's campaign advisers in the 2008 campaign and one of the few Republican strategists to go on the record yesterday, told the Hill magazine: "It's a kidney shot because it reveals a very cynical view. He's pushing independent voters out the door."

He added that it could help motivate disgruntled Democrats into turning out in large numbers for the election.

With seven weeks left, there is still time for Romney to turn it around, with the support of tens of millions of dollars in advertising and a good performance in the debates with Obama, the first scheduled for 3 October in Denver, Colorado.

Romney, who was scheduled to hold fundraising events in Salt Lake City and Dallas on Tuesday, looked uncharacteristically haggard when he held an impromptu press conference on Monday night to deal with the 47% video and offered up a rambling defence. He said he had been speaking "off the cuff" and describing his comments as not "elegantly stated".

While Romney's views expressed in the new excerpt about the Palestinians are not a major surprise given his strong expression of support for the Israeli prime minister Binyanmin Netanyahu, US presidents like to portray themselves as neutral referees in the conflict, even if in fact they lean towards Israel. Romney has blown any lingering prospect of being seen as a neutral arbiter.

"I look at the Palestinians not wanting to see peace anyway, for political purposes, committed to the destruction and elimination of Israel," he said. He suggested he would not actively engage in the promotion of a peace process, as his predecessors have done.

One of the reasons he said that it is difficult to allow the creation of a Palestinian state on the West Bank is that it could then become a base to which Iran and other Arab nations channel rockets and other weapons to threaten the Israeli financial capital Tel Aviv.

Indicating he would not be pushing for a two-state solution, the creation of Palestine to stand alongside Israel, he said: "All right, we have a potentially volatile situation but we sort of live with it, and we kick the ball down the field and hope that ultimately, somehow, something will happen and resolve it."

The Obama administration, apart from a few tentative attempts at the start of his presidency, has made no serious effort to resolve the conflict. The Obama administration has hinted that, free from the constraints of fighting another election, it might take a more robust approach to the issue in a second term.

• This article was amended on 20 September 2012. The original said "He [Mitt Romney] described Tel Aviv as being only seven miles from the West Bank, though in fact it is over 40 miles away." In fact Tel Aviv is about 11 miles away from the nearest point of the West Bank.

Republican presidential candidate Mitt Romney speaks at a hastily-convened press conference after being secretly filmed saying nearly half of all Americans are government-dependent 'victims' who do not pay taxes